Question

The probability that Mason's bus arrives on time is 1/2. 4 If his bus is on time then the probability he arrives at work by 9 am is 3 If his bus is late then the probability he arrives at work by 9 am is. 3 Work out the probability that Mason does not arrive at work by 9 am. Give your answer as a fraction in its simplest form.​

Answer 1

To find the probability that Mason does not arrive at work by 9 am, we need to consider the scenarios where his bus is on time and his bus is late. Using the multiplication rule, the probability is found to be 1/8.

Step-by-step explanation:

To find the probability that Mason does not arrive at work by 9 am, we need to consider the scenarios where his bus is on time and his bus is late. Since the probability that his bus arrives on time is 1/2 and the probability he arrives at work by 9 am given that his bus is on time is 3/4, we can calculate the probability using the multiplication rule:

P(Mason does not arrive at work by 9 am) = [P(bus is on time)] * [P(he arrives at work by 9 am given that bus is on time)] + [P(bus is late)] * [P(he arrives at work by 9 am given that bus is late)]

P(Mason does not arrive at work by 9 am) = (1/2) * (1 - 3/4) + (1/2) * (1 - 3/4) = 1/8

Therefore, the probability that Mason does not arrive at work by 9 am is 1/8.